How do I join a many-faced mesh to a mesh with fewer faces?
You can use Bridge tool.


Select the two loops you want to connect;
Press W, choose Bridge Edge Loops in the popup menu. More options for Bridge tool can be found in F6 menu.






P.S. However, such topology may not benefit Surface Subdivision. So, it's recommended to have even subdivision level for both cup and handle. Suggested workflow would be: